Answer
Local maximum: $0$ at $x=0$
Local minima: $-0.25$ at $x=-0.71$ and at $x=0.71$
$f$ is increasing on: $(-0.71,0)$ and $(0.71,2)$ ;
$f$ is decreasing on: $(-2,-0.71)$ and $(0,0.71 )$
Work Step by Step
(graphed with desmos.com).
A local maximum at x=c exists if there is an interval around c such that f(c) is the largest function value on that interval.
A local minimum at x=c exists if there is an interval around c such that f(c) is the lowest function value on that interval.